Reynolds Stress Closure Including Nonlocal and Nonequilibrium Effects in Turbulent Flows (original) (raw)
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Reynolds stress closure for nonequilibrium effects in turbulent flows
Physics of Fluids, 2008
From consideration of turbulence anisotropy dynamics due to spatial or temporal variations in the mean strain rate, a new Reynolds stress closure for nonequilibrium effects in turbulent flows has been developed. This closure, formally derived from the Reynolds stress anisotropy transport equation, results in an effective strain rate tensor that accounts for the strain rate history to which the turbulence has been subjected. In contrast to prior nonequilibrium models that have sought to address nonequilibrium effects via changes in the eddy viscosity, the present approach accounts for nonequilibrium effects in the fundamental relation between the anisotropy tensor and the strain rate tensor. The time-local form of the nonequilibrium closure can be readily implemented in place of the classical equilibrium Boussinesq closure on which most existing computational frameworks are currently based. This new closure is applied here to four substantially different classes of nonequilibrium test problems. Results show dramatically improved agreement with experimental and computational data, without the need to vary any model parameters, when compared with the standard equilibrium closure and with various prior nonequilibrium closures.
Nonlocal form of the rapid pressure-strain correlation in turbulent flows
Physical Review E, 2009
A new fundamentally-based formulation of nonlocal effects in the rapid pressure-strain correlation in turbulent flows has been obtained. The resulting explicit form for the rapid pressure-strain correlation accounts for nonlocal effects produced by spatial variations in the mean-flow velocity gradients, and is derived through Taylor expansion of the mean velocity gradients appearing in the exact integral relation for the rapid pressure-strain correlation. The integrals in the resulting series expansion are solved for high-and low-Reynolds number forms of the longitudinal correlation function f (r), and the resulting nonlocal rapid pressure-strain correlation is expressed as an infinite series in terms of Laplacians of the mean strain rate tensor. The new formulation is used to obtain a nonlocal transport equation for the turbulence anisotropy that is expected to provide improved predictions of the anisotropy in strongly inhomogeneous flows.
Linear analysis of non-local physics in homogeneous turbulent flows
Physics of Fluids, 2019
Characterization of non-local physical mechanisms is one of the important challenges toward deeper understanding of turbulent flows. In this investigation, we study the role of pressure in the evolution of three-dimensional incompressible homogeneous turbulent flows. We find that the evolution of turbulence, the nature of inertial physics, and pressure action are dependent on the mean flow invariants. We identify and explain the intercomponent energy transfer induced by the rapid pressure strain correlation for different regimes of flow. Additionally, the structuring effect of pressure on turbulent fluctuations of different alignments is determined and explicated. We exhibit that in regimes of flow where the action of the pressure strain correlation is significant, there is a switching of the flow evolution between diametric stages of evolution. This phenomenon is explained, and its lack of amenability to single-point turbulence modeling is detailed.
2009
The computational formulation of a new nonequilibrium Reynolds stress closure is presented along with preliminary validation results for both homogeneous and inhomogeneous turbulent flow problems of practical engineering importance. The new nonequilibrium closure, which has been rigorously derived elsewhere, 1 replaces the classical Boussinesq hypothesis appearing in many current two-equation turbulence models with a comparably simple representation for the Reynolds stresses, thereby allowing straightforward implementation in existing computational frameworks. The new nonequilibrium closure has been extended to include a rigorously derived realizable eddy viscosity, and theoretical details of the closure are evaluated through fundamental tests of periodically and impulsively sheared homogeneous turbulence. The full computational formulation of the nonequilibrium closure is outlined for both k-and k-ω model frameworks. Finally, preliminary inhomogeneous flow results are presented using the k-ω framework for turbulent flow over a flat-plate and the interaction of an impinging oblique shock wave with a turbulent boundary layer.
Local and nonlocal pressure Hessian effects in real and synthetic fluid turbulence
Physics of Fluids, 2011
The Lagrangian dynamics of the velocity gradient tensor A in isotropic and homogeneous turbulence depend on the joint action of the self-streching term and the pressure Hessian. Existing closures for pressure effects in terms of A are unable to reproduce one important statistical role played by the anisotropic part of the pressure Hessian, namely the redistribution of the probabilities towards enstrophy production dominated regions. As a step towards elucidating the required properties of closures, we study several synthetic velocity fields and how well they reproduce anisotropic pressure effects. It is found that synthetic (i) Gaussian, (ii) Multifractal and (iii) Minimal Turnover Lagrangian Map (MTLM) incompressible velocity fields reproduce many features of real pressure fields that are obtained from numerical simulations of the Navier Stokes equations, including the redistribution towards enstrophy-production regions. The synthetic fields include both spatially local, and nonlocal, anisotropic pressure effects. However, we show that the local effects appear to be the most important ones: by assuming that the pressure Hessian is local in space, an expression in terms of the Hessian of the second invariant Q of the velocity gradient tensor can be obtained. This term is found to be well correlated with the true pressure Hessian both in terms of eigenvalue magnitudes and eigenvector alignments.
In this paper, we consider the evolution of decaying homogeneous anisotropic turbulence without mean velocity gradients, where only the slow pressure rate of strain is nonzero. A higher degree nonlinear return-to-isotropy model has been developed for the slow pressure–strain correlation, considering anisotropies in Reynolds stress, dissipation rate, and length scale tensor. Assumption of single length scale across the flow is not sufficient, from which stems the introduction of length scale anisotropy tensor, which has been assumed to be a linear function of Reynolds stress and dissipation tensor. The present model with anisotropy in length scale shows better agreement with well-accepted experimental results and an improvement over the Sarkar and Speziale (SS) quadratic model.
Theoretical and Computational Fluid Dynamics, 2004
Tensor representation theory is used to derive an explicit algebraic model that consists of an explicit algebraic stress model (EASM) and an explicit algebraic heat flux model (EAHFM) for two-dimensional (2-D) incompressible non-isothermal turbulent flows. The representation methodology used for the heat flux vector is adapted from that used for the polynomial representation of the Reynolds stress anisotropy tensor. Since the methodology is based on the formation of invariants from either vector or tensor basis sets, it is possible to derive explicit polynomial vector expansions for the heat flux vector. The resulting EAHFM is necessarily coupled with the turbulent velocity field through an EASM for the Reynolds stress anisotropy. An EASM has previously been derived by Jongen and Gatski [10]. Therefore, it is used in conjunction with the derived EAHFM to form the explicit algebraic model for incompressible 2-D flows. This explicit algebraic model is analyzed and compared with previous formulations including its ability to approximate the commonly accepted value for the turbulent Prandtl number. The effect of pressure-scrambling vector model calibration on predictive performance is also assessed. Finally, the explicit algebraic model is validated against a 2-D homogeneous shear flow with a variety of thermal gradients.
Theoretical and numerical study of highly anisotropic turbulent flows
European Journal of Mechanics - B/Fluids, 2004
We present a detailed numerical study of anisotropic statistical fluctuations in stationary, homogeneous turbulent flows. We address both problems of intermittency in anisotropic sectors, and the relative importance of isotropic and anisotropic fluctuations at different scales on a direct numerical simulation of a three-dimensional random Kolmogorov flow. We review a simple argument to predict the dimensional scaling for all velocity moments, in all anisotropic sectors. We extend a previous analysis made on the same data set (Phys. Rev. Lett. 86 (2001) 4831) presenting (i) the statistical behavior of spectra and co-spectra; (ii) high-order longitudinal structure functions; (iii) anisotropic fluctuations of the full tensorial two-points velocity correlations. Among the many issues discussed, we stress the problem of the return-to-isotropy, the universality of anisotropic fluctuations and the foliation mechanism. A new a priori test on sub-grid quantities used in Large-Eddy Simulations is also presented.
Extraction of Anisotropic Contributions in Turbulent Flows
Physical Review Letters, 1998
We analyze turbulent velocity signals in the atmospheric surface layer, obtained by pairs of probes separated by inertial-range distances parallel to the ground and (nominally) orthogonal to the mean wind. The Taylor microscale Reynolds number ranges up to 20 000. Choosing a suitable coordinate system with respect to the mean wind, we derive theoretical forms for second order structure functions and fit them to experimental data. The effect of flow anisotropy is small for the longitudinal component but significant for the transverse component. The data provide an estimate for a universal exponent from among a hierarchy that governs the decay of flow anisotropy with the scale size.
Non-isotropic dissipation in non-homogeneous turbulence
Journal of Fluid Mechanics
On the basis of the two-point velocity correlation equation a new tensor lengthscale equation and in turn a dissipation rate tensor equation and the pressurestrain correlation are derived by means of asymptotic analysis and frame-invariance considerations. The new dissipation rate tensor equation can account for non-isotropy effects of the dissipation rate and streamline curvature. The entire analysis is valid for incompressible as well as for compressible turbulence in the limit of small Mach numbers. The pressure-strain correlation is expressed as a functional of the two-point correlation, leading to an extended compressible version of the linear formulation of the pressure-strain correlation. In this turbulence modelling approach the only terms which still need ad hoc closure assumptions are the triple correlation of the fluctuating velocities and a tensor relation between the length scale and the dissipation rate tensor. Hence, a consistent formulation of the return term in the pressure-strain correlation and the dissipation tensor equation is achieved. The model has been integrated numerically for several different homogeneous and inhomogeneous test cases and results are compared with DNS, LES and experimental data.